Binomial Formula !!

Question

Use the binomial formula to find the coefficient of the q²s¹³ term in the expansion of (3q-s)¹⁵

Answer 1

The specific term of a binomial expansion (a+b)ⁿ is given by the following formula

(n n-r)*a^r *b^n-r where (n n-r) is equal to n! / (r!*(n-r)!) ! is factorial symbol.

We are considering (3q-s)¹⁵

So a=3q and b=-s

We are looking for term q²s¹³ so in this case we use n=15, r=2, a=3q, b=-s

By the formula, we get 15!/(2!*(13)!)*(3q)² * (-s) ¹³

remember (3q)² = 9q² (-s)¹³ = -s¹³

See what you get when you multiply all terms together!